Phase I of the study calls for a combination of carboplatin given every 3 weeks with weekly paclitaxel. The dose intensity of paclitaxel can be increased considerably by weekly administration with minimal hematological toxicity and in addition, paclitaxel may also have a protective effect on carboplatin induced thrombocytopenia. It is anticpated that the increased dose intensity of paclitaxel in this combination would result in developing an active regimen without added toxicity as seen on a regular every 3-week schedule.